Ancient and modern Hellenic: two different languages or not?

Some foreigners have claimed that the ancient Hellenic language is different from the modern Hellenic in such a way that they are not connected at all. Some others believe that when someone who has as mother language the Hellenic and claims that he also knows the ancient Hellenic, they believe that he speaks two different languages. Others believe that the modern and ancient have a very distant common root so that their connection is lost in the depths of time. Other claims that the modern language has taken some words from the ancient but they are still two different languages. Well the truth is not exactly like that and we will see why in a minute.